Usion Res. Vol. 31, No. 4, pp. 763-765, 1991 0042-6989/91 $3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright 0 1991 Pergamon Press plc LETTER TO THE EDITOR YES, THERE IS A HALF-CYCLE DISPLACEMENT LIMIT FOR DIRECTIONAL MOTION DETECTION VINCENT DI LOLLO and WALTER F. BISCHOF Department of Psychology, University of Alberta, Edmonton, Alberta, Canada T6G 2E9 zyxwvutsrqponmlkjihg (Received 2 I August 1990) Apparent motion of a band-pass filtered ran- dom-dot kinematogram (RDK) is seen in a sequence of two of more frames, where each trailing frame is a translated version of the preceding one. The largest displacement that produces a reliable and correct impression of directional motion is known as D,,,. Current models of biological motion sensors postulate that the range of values that D,,, can assume is limited by half the period of the sensor’s preferred spatial frequency (Adelson 8z Bergen, 1985; Marr & Ullman, 198 1; van Santen & Sperling, 1985; Watson & Ahumada, 1985). In an apparent contradiction of this postulate, values of D,,, considerably greater than the half-period of the image’s lowest spatial fre- quency have been found with isotropically- filtered RDKs (Bischof & Di Lollo, 1990; Cleary & Braddick, 1990). An account of the excessive values of D,,,, consistent with the half-cycle limit, can be given in terms of image frequency components at orientations oblique to the direction of motion. The frequency of such components with respect to the direction of motion is reduced by a factor of cos 8, where 8 is the orientation with respect to the direction of motion. Oblique components can thus raise the value of D,,, beyond the half-period of the filter’s lower cut-off frequency. Cleary and Braddick considered and rejected this option on the basis of results obtained with two sets of RDKs passed by different filters (Cleary & Braddick, 1987, 1990; Cleary, 1987). The two filters had the same centre-frequency (2.66 c/deg) and frequency bandwidth (1.5 octaves), but differed in orientation bandwidth (a). One filter (a = 0 deg) passed only com- ponents with orientation orthogonal to the di- rection of motion; the other (a = 180 deg) passed components at all-notably oblique- orientations. The two sets of stimuli yielded approximately equal mean values of D,,, (0.87 cycles of the centre frequency for a = 0 deg, and 0.96 for a = 180 deg). Equality of outcomes was re- garded as inconsistent with expectations based on off-axis components. That is, any contri- bution to motion detection made by off-axis components should have been evidenced in greater values of D,, for RDKs passed by the 180deg filter. In the absence of such an effect, Cleary and Braddick (1987, 1990) rejected the off-axis account as an explanatory basis for the excessive values of D,,,. In turn, this disconfirms the assumption of the half-cycle limit and impugnes the scope and generality of current models of biological motion sensors. These are weighty conclusions, based on evi- dence of relatively limited scope. To broaden the scope, we need to know to what extent predictions based on the half-cycle limit can account for performance with stimuli varying systematically in frequency and orientation bandwidths. A one-dimensional analysis, lim- ited to single independent motion sensors, is clearly insufficient. What is needed is a two- dimensional scheme capable of describing how the ouputs of populations of sensors combine to produce the observed outcome. In short, we need a model of motion integration. We report such a model and its empirical verification in the target article of the present comments (Bischof & Di Lollo, 1991). In their comment, Braddick and Cleary (199 1) question the sufficiency of our model and data in establishing the half-cycle displacement limit as a general rule of motion perception. 163